Zero-momentum trajectories inside a black hole and high energy particle collisions

Abstract

We consider properties of the trajectory with the zero momentum inside a spherically symmetric black hole. We work mostly in the Painlevé% -Gullstrand frame and use the concept of the "river model of black hole". This consept allows us to decompose (in a "cosmological manner") the geodesic motion of a test particle into a "flow" of the frame and a peculiar motion with respect to this frame. After this decomposition the application of standard formulae of special relativity for kinematic processes becomes possible. The present paper expands the notion of peculiar velocities to the region under the horzion and exploits it for the description of two physical processess - high energy collisions and redshift. Using this approach we (i) present a novel description of particle collisions occuring near black hole horizons inside the event horizon. In particular, we show that the trajectory under discussion is relevant for ultra-high energy collisions. (ii) In the framework of the river model, we derive a simple formula (both outside and inside the horizon) for the redshift in the case of radial motion. It represents the product of two factors. One of them is responsible for pure gravitational part whereas the other one gives the Doppler shift due to peculiar motion with respect to the "flow".

arXiv comment24 pages. Matches published version

References in corpus (15)

• Kerr Black Holes as Particle Accelerators to Arbitrarily High Energy
• Black hole singularities: a numerical approach
• Acceleration of particles as universal property of rotating black holes
• The river model of black holes
• On particle collisions in the gravitational field of the Kerr black hole
• Particle Accelerators inside Spinning Black Holes
• Interior of a Schwarzschild black hole revisited
• Acceleration of particles by black holes: kinematic explanation
• Are black holes totally black?
• Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects
• Acceleration of particles near the inner black hole horizon
• Is the super-Penrose process possible near black holes?
• Black holes and particles with zero or negative energy
• Unified approach to redshift in cosmological /black hole spacetimes and synchronous frame
• Equatorial geodesics in ergoregion of dirty black holes and zero energy observers

Cited by in corpus (8)

• Flow and peculiar velocities for generic motion in spherically symmetric black holes
• On particle dynamics near the singularity inside the Schwarzschild black hole and T-spheres
• General radially moving references frames in the black hole background
• Redshift/blueshift inside the Schwarzschild black hole
• On strategies of motion under the black hole horizon
• Particle decay, Oberth effect and a relativistic rocket in the Schwarzschild background
• Particles of negative and zero energy in black holes and cosmological models
• Dynamics of redshift/blueshift during free fall under the Schwarzschild horizon